The following logic block depicts the controller for a set of holiday decoration lights with different light patterns: A- Holiday Lights Controller B- The controller has the following specification: Outputs: The controller has three output signals L1, L2, and L, that control three different sets of light bulbs. If an output signal is set to 1 then the corresponding set of light bulbs is turned on, and if it is set to 0 then the corresponding set of light bulbs is turned off. Inputs: The controller has two inputs, A and B, which jointly specify the pattern that the lights should follow. Four different patterns are supported: • Off (AB=00): All sets of light bulbs are turned off the entire time. • Brightening (AB=01): The brightness is gradually increased by turning on more light bulbs each cycle then going back to no lights and repeating. In other words, if all lights are initially off, then on the next cycle, the Li lights are turned on. On the next cycle, the L lights are turned on. On the next cycle, the La lights are turned on. On the next cycle, all lights are turned off again. This process keeps repeating. • Dimming (AB=10): The brightness is gradually decreased by turning off more light bulbs each cycle then going back to all lights on and repeating. In other words, if all lights are initially on, then on the next cycle, the La lights are turned off. On the next cycle, the L lights are turned off. On the next cycle, the L, lights are turned off. On the next cycle, all lights are turned on again. This process keeps repeating. O Blinking (AB=11); The lights alternate between being all on and all off. In other words, if all lights are initially off, then on the next cycle, they are all turned on. On the next cycle, they are all turned off. This process keeps repeating. If this input is given at a time when some lights are on and others are off, then the first thing to do is to turn all the lights off and then start alternating. States: The controller has four states represented by two state bits S, and S. These states are: • Level 0 (S,S, = 00): All lights are off • Level 1 (S,S = 01): Only the L, lights are on • Level 2 (S,S = 10): Only the Li and L, lights are on • Level 3 (S,S, = 11): All lights are on Implement the controller as a finite state machine: (1) Draw the state diagram for the controller. (2) Derive the truth table for the output function of the controller and write the logic equations for the output function. (3) Derive the truth table for the next-state function of the controller. (4) Use a K-map to minimize the equations for the next-state function and write the simplified logic equations for the next state function. (5) Draw a circuit diagram depicting the implementation of the controller.

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Chapter1: Introduction
Section: Chapter Questions
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The following logic block depicts the controller for a set of holiday decoration lights with different light
patterns:
A
Holiday
Lights
Controller
B
The controller has the following specification:
Outputs: The controller has three output signals L1, L2, and Ls that control three different sets of
light bulbs. If an output signal is set to 1 then the corresponding set of light bulbs is turned on,
and if it is set to 0 then the corresponding set of light bulbs is turned off.
• Inputs: The controller has two inputs, A and B, which jointly specify the pattern that the lights
should follow. Four different patterns are supported:
• Off (AB=00): All sets of light bulbs are turned off the entire time.
o Brightening (AB=01): The brightness is gradually increased by turning on more light bulbs
each cycle then going back to no lights and repeating. In other words, if al lights are
initially off, then on the next cycle, the Li lights are turned on. On the next cycle, the e
lights are turned on. On the next cycle, the La lights are turned on. On the next cycle, all
lights are turned off again. This process keeps repeating.
• Dimming (AB=10): The brightness is gradually decreased by turning off more light bulbs
each cycle then going back to all lights on and repeating. In other words, if all lights are
initially on, then on the next cycle, the Ls lights are turned off. On the next cycle, the L
lights are turned off. On the next cycle, the L, lights are turned off. On the next cycle, all
lights are turned on again. This process keeps repeating.
• Blinking (AB=11): The lights alternate between being all on and all off. In other words, if
all lights are initially off, then on the next cycle, they are all turned on. On the next cycle,
they are all turned off. This process keeps repeating. If this input is given at a time when
some lights are on and others are off, then the first thing to do is to turn all the lights off
and then start alternating.
States: The controller has four states represented by two state bits S, and Sz. These states are:
o Level 0 (S;S = 00): All lights are off
o Level 1 (S,S, = 01): Only the Li lights are on
Level 2 (S;S = 10): Only the Li and La lights are on
• Level 3 (S,S = 11): All lights are on
Implement the controller as a finite state machine:
(1) Draw the state diagram for the controller.
(2) Derive the truth table for the output function of the controller and write the logic equations for
the output function.
(3) Derive the truth table for the next-state function of the controller.
(4) Use a K-map to minimize the equations for the next-state function and write the simplified logic
equations for the next state function.
(5) Draw a circuit diagram depicting the implementation of the controller.
Transcribed Image Text:The following logic block depicts the controller for a set of holiday decoration lights with different light patterns: A Holiday Lights Controller B The controller has the following specification: Outputs: The controller has three output signals L1, L2, and Ls that control three different sets of light bulbs. If an output signal is set to 1 then the corresponding set of light bulbs is turned on, and if it is set to 0 then the corresponding set of light bulbs is turned off. • Inputs: The controller has two inputs, A and B, which jointly specify the pattern that the lights should follow. Four different patterns are supported: • Off (AB=00): All sets of light bulbs are turned off the entire time. o Brightening (AB=01): The brightness is gradually increased by turning on more light bulbs each cycle then going back to no lights and repeating. In other words, if al lights are initially off, then on the next cycle, the Li lights are turned on. On the next cycle, the e lights are turned on. On the next cycle, the La lights are turned on. On the next cycle, all lights are turned off again. This process keeps repeating. • Dimming (AB=10): The brightness is gradually decreased by turning off more light bulbs each cycle then going back to all lights on and repeating. In other words, if all lights are initially on, then on the next cycle, the Ls lights are turned off. On the next cycle, the L lights are turned off. On the next cycle, the L, lights are turned off. On the next cycle, all lights are turned on again. This process keeps repeating. • Blinking (AB=11): The lights alternate between being all on and all off. In other words, if all lights are initially off, then on the next cycle, they are all turned on. On the next cycle, they are all turned off. This process keeps repeating. If this input is given at a time when some lights are on and others are off, then the first thing to do is to turn all the lights off and then start alternating. States: The controller has four states represented by two state bits S, and Sz. These states are: o Level 0 (S;S = 00): All lights are off o Level 1 (S,S, = 01): Only the Li lights are on Level 2 (S;S = 10): Only the Li and La lights are on • Level 3 (S,S = 11): All lights are on Implement the controller as a finite state machine: (1) Draw the state diagram for the controller. (2) Derive the truth table for the output function of the controller and write the logic equations for the output function. (3) Derive the truth table for the next-state function of the controller. (4) Use a K-map to minimize the equations for the next-state function and write the simplified logic equations for the next state function. (5) Draw a circuit diagram depicting the implementation of the controller.
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